Displaying similar documents to “A simple approach to functional inequalities for non-local Dirichlet forms”

A natural derivative on [0, n] and a binomial Poincaré inequality

Erwan Hillion, Oliver Johnson, Yaming Yu (2014)

ESAIM: Probability and Statistics

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We consider probability measures supported on a finite discrete interval [0, ]. We introduce a new finite difference operator ∇, defined as a linear combination of left and right finite differences. We show that this operator ∇ plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting as eigenfunctions of the relevant operator. We briefly discuss the relationship of this operator to the problem of...

Detecting abrupt changes in random fields

Antoine Chambaz (2010)

ESAIM: Probability and Statistics

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This paper is devoted to the study of some asymptotic properties of a -estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes recovery of sets. It involves various techniques, including -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply...

Entropy maximization and the busy period of some single-server vacation models

Jesus R. Artalejo, Maria J. Lopez-Herrero (2010)

RAIRO - Operations Research

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In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in vacation models operating under the -, - and -policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable...

Asymptotic equipartition properties for simple hierarchical and networked structures

Kwabena Doku-Amponsah (2012)

ESAIM: Probability and Statistics

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We prove for simple hierarchical structures (modelled as ) and networked structures (modelled as ). For example, for large , a networked data structure consisting of units connected by an average number of links of order   log  can be coded by about  ×  bits, where is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.

Asymptotic equipartition properties for simple hierarchical and networked structures

Kwabena Doku-Amponsah (2012)

ESAIM: Probability and Statistics

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We prove for simple hierarchical structures (modelled as ) and networked structures (modelled as ). For example, for large , a networked data structure consisting of units connected by an average number of links of order   log  can be coded by about  ×  bits, where is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem         inf{ () +  () + (1 −  − ) () | Ω open in ℝ, || ≤ 1}, for  ∈ [0, 1],  +  ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

Constraints on distributions imposed by properties of linear forms

Denis Belomestny (2010)

ESAIM: Probability and Statistics

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Let () be independent identically distributed bivariate vectors and , are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of and imply the same property for and , and under what conditions does the independence of and entail independence of and ? Some analytical sufficient conditions...

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Lorenzo Brasco (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We generalize to the -Laplacian a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of of a set in terms of its -torsional rigidity. The result is valid in every space dimension, for every 1    ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants....